A mathematical model of the acute myeloblastic leukemic state has been formulated which reproduces in a quantitative manner the known kinetic aspects of this disease state. A mathematical representation of a cell cycle specific drug-treatment regimen will now be superimposed on the model, which is designed to accurately represent the lethal action of known drugs. By varying parametrically such features as the frequency of drug treatment, we shall attempt to determine an optimal drug-treatment regimen which maximizes the killing of neoplastic cells and minimizes the killing of normal cells, by taking advantage of their different kinetic properties. The above project requires solutions of nonlinear differential equations obtained with the aid of a computer. Our results will subsequently be correlated with actual clinical experiences, with the goal of providing a rational basis for improving drug-treatment regimens in cancer chemotherapy.